You have to put effort into making an experience with psylocybin meaningful and helpful. It could go wrong very easily, especially for those who are in a difficult situation or headspace. (Speaking from experience.)
As for SSRIs? Safe, effective, with a handful of annoying side effects. Straightforward to use, low potential for misuse, requires sustained use for any intended effects. A doctor who already has familiarity with a patient's mild or moderate symptoms of anxiety or depression may very well just prescribe one if asked and if not contraindicated. Not that you should randomly start popping Prozac, but it's unlikely to hurt you if you did.
Ask your doctor, try the things that doctors currently believe are most likely to work first. If for whatever reason you choose to go beyond the current medical consensus, please stay safe and keep your doctor up to date.